This blog is about Python Power Electronics - a free and open source software for power electronics and power systems professionals. Aimed at providing education about power electronics application specifically to renewable energy and smart grids, the software will be accompanied by simulation examples, short reports and presentations. The software can found on the website http://www.pythonpowerelectronics.com/.

Friday, March 8, 2013

Stiff systems

Changing the title at least to reflect the focus of the problem.

Change in strategy. Make a collection of branches and for each branch have the entries for A, E and B matrices. So this will give an indication of the L, R and V values in every branch.

What is a stiff branch?

It is not a branch with negligible or zero inductance. If the resistance is small enough, it could be a load resistance or even a branch resistance.

It is a branch with a large resistance and negligible or zero inductance.

So, how do know this? It is relative. If all the resistances in the circuit are in a narrow range - say 0.1 to 1000, the system is not stiff. How large a resistance is again depends on the voltage level - for a 120 V system, 100 kiloohm would be large, for a 120 kV system, it would be nothing. But to avoid a per unit system and still classify a system as stiff will mean I need to arrange them in an order according to the resistances. Which is not a difficult task.

After this, I need to calculate the L/R ratio just in case though a very large inductance accompanying a large resistance is not very practical. A large resistance simply means an open circuit or a non-conducting medium but a large inductance means a huge core and a large number of turns in the winding. The worst I can think of in a huge transformer that has a large magnetising inductance but this will have a low winding resistance and a large core loss resistor across it. So it won't be a stiff system. On the contrary it will be a system with a large time constant which is actually the case because when you energize one of these monsters, the magnetizing current can take a long time to decay.

The smallest resistance and inductance would really be the measure of a circuit because they would be the parasitics. So suppose I take these as a base and try to calculate ratios of other elements with respect to it. So a parasitic resistance of 0.005 ohm for a 120 V circuit would be acceptable wire resistance. And a 10 ohm load resistor would result in a ratio of 10/0.005=2000 which is quite OK. But a 1 megaohm resistor would result in a ratio 2.0e+8 which should raise an alarm.

Taking such a ratio is itself a form of per unit, just that the per unit is arbitrary and if a user puts ridiculous values and an equally impractical simulation time step, a circuit will classified as stiff.